Abstract
We use the Foldy-Wouthuysen representation to construct Lorentz-invariant interactions of heavy fields, building the interactions starting from non-relativistic heavy particle fields. We show that the couplings obtained feature a straightforward 1/m, where m is the mass of the heavy particle, expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications on the examples of pion-nucleon and pion-nucleon-delta couplings in chiral effective field theory. For instance, we show that one of the terms usually considered to be a part of chiral index-1 πNΔ vertex is redundant. We discuss the implications of this fact.
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